None-ambiguous reading systems for analog-to-digital converters

ABSTRACT

Reading system free from ambiguity of reading at the boundary of two digits in which two n-digits code disks representing higher order digits and lower order digits are employed and three successive signals from said higher order code disk which generate signals, adjacent two signals of which partially overlap each other, and two signals generated from said lower order disk respectively representing any digits in the higher half and lower half of n-digits are fed to a logical circuit performing a particular logical operation.

United States Patent i 1 lnvcnwr Ymlm Nlfllkiyo 511 int. Cl G08c 9/04 ew-J m 50 Field of Search 340/347, [2i] Appl. No. 844,339 357, 358; 250/233 [22] Filed July 24, 1969 [45] Patented Sept. 7, 1971 [56] References Cited [73] Assignee Okurna Medina-y Works Ltd. UNITED STATES PATENTS 7s 6 1 N k 4 7 Priority J 3,4 ,34 11/ 969 Yasumasa aru ryo..... 3 0/34 33 1., Primary Examiner-Maynard R. Wilbur 3 1 3 333, Assirtant Examiner-Charles D. Miller c m mm m s Attorney-Waters, Roditi, Schwartz & Nissen 376,689, June 22, 1964, now Patent No. 3,478,346.

ABSTRACT: Reading system free from ambiguity of reading at the boundary of two digits in which two n-digits code disks representing higher order digits and lower order digits are employed and three successive signals from said higher order RE n code disk which generate signals, adjacent two signals of [54] AL g h g FOR which partially overlap each other, and two signals generated a Cl l 19 Drawing m from said lower order disk respectively representing any digits in the higher half and lower half of n-digits are fed to a logical [52] US. (I 340/347 P circuit performing a particular logical operation.

VI L V W 0 PATENTED str 1 am 3, 603. 97 8 SHEET 5 OF T To /7 order code dis/r SHA P/IVG o/rr SHAPING C/(T Z SHAPING C/(T 4 Z SHAP/NG o/(r sHAP/No 0/0 [0 9 SHAPING C/(T 9 From /ower order code dis/r NONE-AMBIGUOUS READING SYSTEMS FOR ANALOG- TO-DIGITAL CONVERTERS CROSS-REFERENCES TO RELATED APPLICATIONS This application is acontinuation-in-part application of my earlier application Ser. No. 376,689, filed June 22, 1964, and now U. S. Pat. No. 3,478,346.

BACKGROUND OF THE INVENTION 1. Field of the Invention This invention relates to reading systems of analog-to-digital converters for converting analog quantities, such as angles of rotation and so on into digital quantities.

2. Description of the Prior Art In general, a code disk, forming the main part of an analogto-digital converter, is subject to being erroneously read at boundaries between adjacent digits on the code disk. Thus, due to inevitable minor errors, such as caused by unevenness of end conditions of the code disk and brushes and so on whether 9 is read or is read is, for example, governed by chance, this resulting in numerous errors.

There have been various contrivances proposed for preventing errors, for example, greater than one digit. Particularly, there have been utilized a code disk of alternate or binary code, a Gray Code disk, a special reading brush arrangement such as a dual-brush system, V-brush system, and the like.

SUMMARY OF THE INVENTION An object of the present invention is to provide a novel reading system of high precision, which is simple in construction and low in cost, preserving the advantages of noncontact point technique of the prior art.

According to the present invention, a code disk capable of supplying signals of a required number of digits is employed for providing signals successively overlapping in time, which are introduced i n to a logical circuit satisfying the logical equaerroneous signal is prevented.

BRIEF DESCRIPTION OF THE DRAWING FIG. 1 is an elevational view of a noncontact-type code 'plate or disk embodying the present invention;

FIG. 2 is a longitudinal sectional view of the disk shown in FIG. 1;

' FIG. 3 is a graph showing the relation between an angle of relative rotation of the disk and a secondary voltage induced therein;

FIG. 4 is an elevational view of a contact-type code disk embodying the invention;

FIG. 5 is a longitudinal sectional view of the disk shown in FIG. 4;

FIGS. 6a to 6d are block diagrams of logical circuits according to the invention;

FIG. 7 is a graph showing wave forms at various parts of the logical circuit of FIG. 6;

FIGS. 8a and 8b are block diagrams of logical circuits according to the invention for a decimal code disk and disks, respectively;

FIG. 9 is a block diagram of a logical circuit according to the invention for five-decimal code disks; and

FIGS. 10a 10f are graphs for illustrating time-sharing operation.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Let us consider a code disk for providing 10 decimal digits per rotation of the disk shaft by way of example. If two such disks are used. and the rotating shafts are coupled together with a great ratio oi l0 l. the input shalt can provide 100 digits. In this case, when the lower order shaft is at the boundary between 9 and "0, the higher order shaft should be at the boundary between adjacent digits, and'the change of the higher order shaft byone digit and the change of the lower order shaft from 9 to 0" should be coincident in position with regard to time. However, it is generally impossible to accomplish this coincidence because of mechanical inaccuracy, and erroneous signals are apt occur. For example, an incorrect reading of l7, l8," l9," l0, 20," 21, can be effected on rotation of the input shaft.

The present invention prevents such an error from occurring. Thus, referring to FIGS. 1 and 2, the code disk shown comprises a stator 6 carrying uniformly spaced magnetic poles 1 along the outer periphery, the poles extending inwardly towards the center of disk.

Each pole 1 carries a secondary coil 2 wound thereon. The stator 6 also has a boss around which a primary coil 3 is wound. A rotating shaft 5 rotatably passes through the boss of stator 6 and carries a rotatable magnetic piece 4 fixed to the shaft, and having a circumferential width larger than that of each pole 0, I, II, III

When the primary coil 3 is energized and the shaft 5 is rotated, with the magnetic piece 4 successively passing in front of poles 1 each carrying the secondary coil 2, with a magnetic circuit K (FIG. 2) completed and opened successively, voltages are successively induced in the secondary coils 2 as shown in FIG. 3 by [-1 I, L+1' which overlap one another with respect to time. These voltages are introduced into a shaping circuit such as a Schmitt trigger circuit, to provide successively overlapping signals, I-l, 1, 1+1, as shown in FIG. 3, with a line F as the operating point, These signals are introduced into the logical circuit shown in FIG. 6a, 6b, 6c or 6d.

The logical circuit of FIG. 6a, which performs the logical operation L=J-(Crl l+Crl +l,-l$l), comprises NOR circuits T, T T T T T,, T, and T The NOR circuit is a circuit in which, when a signal A is received as an input signal, the circuit delivers a signal A as an output signal, and wh e1 the input signal is A, B, and C, its output is A+B+C, i.e. A-B-C. In other words, the NOR circuit is the combination of a NOT circuit and an OR circuit. The symbols l-l, l, and I+I represent any successive digital signals signals such as 0, l, 2; 5, 6, 7; 9, 0, l and the like which are obtained by shaping the output of each pole of the higher order code disk as shown in FIG. 3, whereas the symbols l1,l, and [+1 represent inverted signals thereof. C, and I represent signals from the lower code disk which will hereinafter be referred to as carry signals for thesakeof can: venience. C, can be a signal generated when the magnetic piece 4 passes a pole of the lower code disk according to any one of successive digits including 9 taken from 5 to 9, for example 6,789, and 1,, can be that of successive digits including 0 taken from 0 to 4, for example 0123. However, it is preferable to take 56,789 and 01,234 for C, and 1,, signal generation, respectively, because this selection enables to make tolerance of the coupling erro of the higher order digits and the lower order digits larger. C, and I represent inverted signals of C, and I,

Now, referring to FIGS. 1 and 3, if the outputs of the poles 0, I and II of the higher order A-D converter are taken to be [-1, l, and 1+1, respectively, and if the carry signals C, and I, are arranged to be generated when the lower order A-D converter outputs are 6 to 9 and 0 to 3, respectively, the wave shape of each part of the logical circuit of FIG. 6a which is reading out the output signal of the pole I varies as shown in FIG. 7 when the movable piece 4 moves in the increasing number direction.

In FIG. 7, character S represents the position of the movable piece of 4 of the higher order A-D converter. It it is assumed that the output of the lower order A-D converter is 9, the higher order converter is delivering both sigrnalsl-i an d I The aforementioned logical equation L =l-(C,-I-l+C,-I,, +l,,-1+ I) is the logical equation for reading out the output I of the higher order converter. Since the signal C, as well as the signal l-l is being delivered at the position 8, the equation L is not satisfied. When the movable piece 4 moves in the increasing number direction and the lower order digit changes from 9 to 0, the signal C, disappears, but instead the signal 1,, appears. consequentlyl-l 'lTl of the NOR circuit T is satisfied resulting in the generation of the signal L. If the movable piece moves further and the lower order digit changes from 30to 4, the signal 1,, disappears, and hence the term I-I,,-I+l is no longer satisfied. However, since I-C,'I,, of the NOR circuit T is satisfied, the signal L is maintained. If the lower order digit changes from 5 to 6 as a result of a further movement of the movable p i e ce, the term I-C ,-l,, is no longer satisfied, but instead lC,-!l of the NOR circuit T is satisfied, and hence the signal L is still maintained. However, if the lower digit changes from 9 to 0 with a further movement of the movable piece, all the terms of the logical equation are no longer satisfied, and hence the signal L disappears. Thus, the logical equation of the signal L is satisfied when the lower order digit is from 0 to 9 within the region of the higher order signal I, and hence the output signal L of the logical circuit of FIG. 6a exactly represents the position of the pole I of the higher order converter.

FIG. 6a shows the logical circuit for reading out the signal of the pole l of the higher order A-D converter. For decimalism, the position of each pole of the higher order A-D converter can be exactly read out by employing such circuits as shown in FIG. 6a.

FIG. 8a shows such a logical circuit for a decimal converter disk. In FIG. 8a, lower left input terminals 0, 3 and 6, 9 are merely connected through respective shaping circuits to the corresponding poles of the lower (or the lowest when more than two code disks are employed) order code disk, respectively. Upper left output terminals C, and I are connected to input terminals C, and 1,, respectively, of the similar logical circuit for the next higher order code disk when more than two code disks are employed, at which time 1,000 or more digits are available. Input terminals 0, 9 are connected to the poles of the higher order code disk corresponding to digits 0, 9, respectively, through respective shaping circuits.

When the carry signals C, and I, satisfy the condition C,=l t he above mentioned logical equation becomes L =l-(C,-I l+C,-l+l Thus, by employing the carry signals C, and I the tolerance of the coupling of the lower order and the higher order digits can be made great. This is one of the outstanding features of the invention.

In the above description, the logical operation has been explained with reference to the logical circuit of FIG. 6a. However, instead of the logical circuit of FIG. 6a, either one of the logical circuits shown in FIGS. 6b to 6d can similarly be employed. The circuit of FIG. 6b comprises three NOR circuits and one OR circuit. The circuit of FIG. 6c comprises four NAND circuits, and the circuit of FIG. 6d comprises three AND circuits and one OR circuit.

lf digits are to be read from, for example, five code disks, five such circuits as shown in FIG. 8a are employed as shown in FIG. 9. Thus, if the number of code disks increases, the logical circuit for reading the digits becomes correspondingly complicated and expensive. However, if a time-sharing technique is employed, the reading can be effected with only one such logical circuit as shown in FIG. 8a.

If such logical circuit as shown in FIG. 8a is successively switched from a code disk to the next higher order code disk, to the highest order code disk, to the lowest order code disk, and so on with a train of timing pulses with intervals of, for example, several microseconds, the outputs from the logical circuit for respective code disks will be as shown in FIG. 10 which illustrates the case of five code disks employed. In this case, although the signal for each digit is actually discrete, practically it can be regarded as a continuous one because each time duration of 1,, r t, is such a short duration as several microseconds.

When only one logical circuit is employed in a time-sharing manner as has just been described for reading digits from any number of code disks, there is the problem that a time difference by one time interval between adjacent timing pulses exists between the readings of one code disk and the next higher order code disk. However, this difficulty can easily be overcome by delaying the carry signals I and C, from each code disk by one time interval by employing a delay circuit as is shown in FIG. 8b. Thus, by connecting each input terminal of the logical circuit of FIG. 8b with all the code disks in common, the digits of all the code disks can be read with only one logical circuit as shown in FIG. 8b.

Referring to FIGS. 4 and 5, when a contact-type code disk 12 is shown as a decimal code disk, it may be such that the circle is divided circumferentially into 10 parts, with conductors l l of 36 spacing for one digit overlapping one another by 18 and insulated from one another by about a 54 width. The

disk 12 carries a central shaft 15 rotatably, which in turn carries a movable piece 14 having contact brushes I3 fixed to the outer end thereof. When the movable piece 14 is rotated with brushes l3 engaging conductors ll successively, the signals from respective are on and off signals, the same as shown in FIG. 3. These signals are applied to the logical circuit of FIG. 6a, 6b, 60 or 6d, and L signals are obtained from an output terminal just as in the first embodiment shown in FIGS. 1 and 2.

With the above-mentioned construction of the present invention, there is no danger of erroneous reading, and no limit to number of digits which can be employed. The invention is particularly useful for decimalism and is not limited to on" and off types of signalling.

According to experiments, the width of each digit may vary by :20 percent, without affecting the operation. Particularly for noncontact types of reading, there are no sliding parts that would affect the useful life and, moreover, high-speed reading is possible.

I claim:

1. A system for reading digits from an analog-to-digital converter having at least two n-digits notation code disks, n being larger than two, said system comprising m sets of n logical circuits, m being the number of said n-digits notation code disks, the l-th circuit of s ai d logical circuits performing the logical operation L--l-(C,-Il+C,-l,,+l,,-l+l) where L is the signal corresponding to any digit signal I generated from the higher order code disk of successive two code disks of said at least two n-digits notation code disks, C, is a carry signal generated when one signal included in the upper group of output signals from the lower order code disk of said two code disks appears and l, is a carry signal generated when one signal included in the lower group of outputs from said lower order code disk appears, said outputs of said lower code disk being divided into said upper and lower groups, said l-th logical circuit having C, and 1,, input terminals for respectively receiving said carry signals C, and I from said lower code disk and I-l l and 1-H input terminals for respectively receiving three successive digit signals 1-1, I and [H from said higher order code disk and L output terminal for deriving therefrom said signal corresponding to said digit signal I, said C, and 1, input terminals of each of said n logical circuits of the set corresponding to said higher order code disk being supplied with said carry signals C, and I, from the set of n logical circuits corresponding to said lower order code disk, each of said logical circuits comprising a first NOR circuit coupled to said I, C, and 1-1 input terminals, a second NOR circuit coupled to said I, C, and l 0 input terminals, a third NOR circuit coupled to said 1, l and [+1 input terminals, and an OR circuit coupled to said first, second and third NOR circuits.

2. A system for reading digits from an analog-to-digital converter having at least two n-digits notation code disks, n being larger than two, said system comprising m sets of n logical circuits, m being the number of said n-digits notation code disks, the l-th circuit of n logical c ircuits performing the logical operation L=l'(C,-l-l+C,-E+I,,-l+l) where L is the signal corresponding to any digit signal 1 generated from the higher order code disk of successive two code disks of said at least two n-digits notation code disks, C, is a carry signal generated when one signal included in the upper group of output signals from the lower order code disk of said two code disks appears, and I is a carry signal generated when one signal included in the lower group of outputs from said lower order code disk appears, said outputs of said lower code disk being divided into said upper and lower groups, said I-th logical circuit having C, and I, input terminals for respectively receiving said carry signals C, and I, from said lower code disk and [-1, I and 1+] input terminals for respectively receiving three successive digit signals [-1, I and [+1 from said higher order code disk and L output terminal for deriving therefrom said signal corresponding to said digit signal I, said C, and 1,, input terminals of each of said n logical circuits of the set corresponding to said higher order code disk being supplied with said carry signals C, and I, from the set of n logical circuits corresponding to said lower order code disk, each of said logical circuits comprising a first NAND circuit coupled to said I, C, and [-1 input terminals, a second NAND circuit coupled to said I, C, and 1,, input terminals, a third NAND circuit coupled to said I, I, and [+1 input terminals, and a fourth NAND circuit coupled to said first, second and third NAND circuits.

3. A system for reading digits from an analog-to-digital converter having at least two n-digits notation code disks, n being larger than two, said system comprising m sets of n logical circuits, m being the number of said n-digits notation code disks, the l-th circuit of sa 'd n l ogical ggcuits performing the logical operation L=I-(C,-Il+C,-I,,+l,,-I+l) where L is the signal corresponding to any digit signal I generated from the higher order code disk of successive two code disks of said at least two n-digits notation code disks, C, is a carry signal generated when one signal included in the upper group of output signals from the lower order code disk of said two code disks appears, and I, is a carry signal generated when one signal included in the lower group of outputs from said lower order code disk appears, said outputs of said lower code disk being divided into said upper and lower groups, said l-th logical circuit having C, and 1,, input terminals for respectively receiving said carry signals C, and 1,, from said lower code disk and ll, I andl+1 input terminals for respectively receiving three successive digit signals [-1, I and [+1 from said higher order code disk and L output terminal for deriving therefrom said signal corresponding to said digit signal I, said C, and 1,, input terminals of each of said n logical circuits of the set corresponding to said higher order code disk being supplied with said carry signals C, and I from the set of n logical circuits corresponding to said lower order code disk, each of said logical circuits comprising a first AND circuit coupled to said I, C, and Il input terminals, a second AND circuit coupled to said I C, and 1,, input terminals, a third AND circuit coupled to said I, 1,, and I+l input terminals, and an OR circuit coupled to said first, second and third AND circuits.

4. A system for reading digits from an analog-to-digital converter having at least two n-digits notation code disks, n being larger than two, said system comprising a set of n logical circuits, a delay circuit and a switching circuit, the I-th circuit of said n l c cal circuits performing the logical operation L=l'( C, 'FT+C,'? +I,,-I+I) where L is the signal corresponding to any digit signal I generated from the higher order code disk of successive two code disks of said at least two n-digits notation code disks, C, is a carry signal generated when one signal included in the upper group of output signals from the lower order code disk of said two code disks appears, and I, is a carry signal generated when one signal included in the lower group of outputs from said lower order code disk appears, said outputs of said lower code disk being divided into said upper and lower groups, said I-th logical circuit having C, and I, input terminals for respectively receiving said carry signals C, and I, from said lower code disk and I-l, I and 1+1 input terminals for respectively receiving three successive digit signals ll, I and [+1 from said high order code disk and L output terminal for deriving therefrom said signal corresponding to said digit signal I, said C, and 1,, input terminals of each of said n logical circuits being supplied with said carry signals C, and 1,, from said L output terminal through said delay circuit, said switching circuit switching connections from said input terminals to said code disks from one code disk to another code disks with predetermined time intervals.

5. A system for reading digits from an analog-to-digital converter according to claim 4, wherein each of said logical circuits comprises first, second and third NOR circuits respectively coupled to said I, C, and 1,, input terminals, a fourth NOR circuit coupled to said ll input terminal and to said first and second NOR circuits, a fifth NOR circuit coupled to said C, and 1, input terminals and to said first NOR circuit, a

sixth NOR circuit coupled to said I+l input terminal and to said first and third NOR circuits, a seventh NOR circuit coupled to said fourth, fifth and sixth NOR circuits, and an eighth NOR circuit coupled to said seventh NOR circuit.

6. A system for reading digits from an analog-to-digital converter according to claim 4, wherein each of said logical circuits comprises a first NOR circuit coupled to said I, C, and [-1 input terminals, a second NOR circuit coupled to said I, C, and 1,, input terminals, a third NOR circuit coupled to said I, I, and [+1 input terminals, and an OR circuit coupled to said first, second and third NOR circuits.

7. A system for reading digits from an analog-to-digital converter according to claim 4, wherein each of said logical circuits comprises a first NAND circuit coupled to said I, C, and [-1 input terminals, a second NAND circuit coupled to said I, C, and 1,, input terminals, a third NAND circuit coupled to said I, 1,, and [+1 input terminals, and a fourth NAND circuit coupled to said first, second and third NAND circuits.

8. A system for reading digits from an analog-to-digital converter according to claim 4, wherein each of said logical circuits comprises of first AND circuit coupled to said I, C, and [-1 input terminals, a second AND circuit coupled to said I, C, and 1,, input terminals, a third AND circuit coupled to said I, I, and [+1 input terminals, and an OR circuit coupled to said first, second and third AND circuits. 

1. A system for reading digits from an analog-to-digital converter having at least two n-digits notation code disks, n being larger than two, said system comprising m sets of n logical circuits, m being the number of said n-digits notation code disks, the l-th circuit of said logical circuits performing the logical operation L l.(Cr.l-1+ Cr.l0+ lo.l+l) where L is the signal corresponding to any digit signal l generated from the higher order code disk of successive two code disks of said at least two n-digits notation code disks, Cr is a carry signal generated when one signal included in the upper group of output signals from the lower order code disk of said two code disks appears and lo is a carry signal generated when one signal included in the lower group of outputs from said lower order code disk appears, said outputs of said lower code disk being divided into said upper and lower groups, said l-th logical circuit having Cr and lo input terminals for respectively receiving said carry signals Cr and lo from said lower code disk and l-1, l and l+1 input terminals for respectively receiving three successive digit signals l-1, l and l+1 from said higher order code disk and L output terminal for deriving therefrom said signal corresponding to said digit signal l, said Cr and lo input terminals of each of said n logical circuits of the set corresponding to said higher order code disk being supplied with said carry signals Cr and lo from the set of n logical circuits corresponding to said lower order code disk, each of said logical circuits comprising a first NOR circuit coupled to said l, Cr and l-1 input terminals, a second NOR circuit coupled to said l, Cr and lo input terminals, a third NOR circuit coupled to said l, lo and l+1 input terminals, and an OR circuit coupled to said first, second and third NOR circuits.
 2. A system for reading digits from an analog-to-digital converter having at least two n-digits notation code disks, n being larger than two, said system comprising m sets of n logical circuits, m being the number of said n-digits notation code disks, the l-th circuit of said n logical circuits performing the logical operation L l.(Cr.l-1+ Cr.l0+ lo.l+1) where L is the signal corresponding to any digit signal l generated from the higher order code disk of successive two code disks of said at least two n-digits notation code disks, Cr is a carry signal generated when one signal included in the upper group of output signals from the lower order code disk of said two code disks appears, and lo is a carry signal generated when one signal included in the lower group of outputs from said lower order code disk appears, said outputs of said lower code disk being divided into said upper and lower groups, said l-th logical circuit having Cr and lo input terminals for respectively receiving said carry signals Cr and lo from said lower code disk and l-1, l and l+1 input terminals for respectively receiving three successive digit signals l-1, l and l+1 from said higher order code disk and L output terminal for deriving therefrom said signal corresponding to said digit signal l, said Cr and lo input terminals of each of said n logical circuits of the set corresponding to said higher order code disk being supplied with said carry signals Cr and lo from the set of n logical circuits corresponding to said lower order code disk, each of said logical circuits comprising a first NAND circuit coupled to said l, Cr and l-1 input terminals, a second NAND circuit coupled to said l, Cr and lo input terminals, a third NAND circuit coupled to said l, lo and l+1 input terminals, and a fourth NAND circuit coupled to said first, second and third NAND circuits.
 3. A system for reading digits from an analog-to-digital converter having at least two n-digits notation code disks, n being larger than two, said system comprising m sets of n logical circuits, m being the number of said n-digits notation code disks, the l-th circuit of said n logical circuits performing the logical operation L l.(Cr.l-1+ Cr.l0+ lo.l+1) where L is the signal corresponding to any digit signal l generated from the higher order code disk of successive two code disks of said at least two n-digits notation code disks, Cr is a carry signal generated when one signal included in the upper group of output signals from the lower order code disk of said two code disks appears, and lo is a carry signal generated when one signal included in the lower group of outputs from said lower order code disk appears, said outputs of said lower code disk being divided into said upper and lower groups, said l-th logical circuit having Cr and lo input terminals for respectively receiving said carry signals Cr and lo from said lower code disk and l-1, l and l+1 input terminals for respectively receiving three successive digit signals l-1, l and l+1 from said higher order code disk and L output terminal for deriving therefrom said signal corresponding to said digit signal l, said Cr and lo input terminals of each of said n logical circuits of the set corresponding to said higher order code disk being supplied with said carry signals Cr and lo from the set of n logical circuits corresponding to said lower order code disk, each of said logical circuits comprising a first AND circuit coupled to said l, Cr and l-1 input terminals, a second AND circuit coupled to said l, Cr and lo input terminals, a third AND circuit coupled to said l, lo and l+1 input terminals, and an OR circuit coupled to said first, second and third AND circuits.
 4. A system for reading digits from an analog-to-digital converter having at least two n-digits notation code disks, n being larger than two, said system comprising a set of n logical circuits, a delay circuit and a switching circuit, the l-th circuit of said n logical circuits performing the logical operation L l.(Cr.l-1+ Cr.l0+ lo.l+1) where L is the signal corresponding to any digit signal l generated from the higher order code disk of successive two code disks of said at least two n-digits notation code disks, Cr is a carry signal generated when one signal included in the upper group of output signals from the lower order code disk of said two code disks appears, and lo is a carry signal generated when one signal included in the lower group of outputs from said lower order code disk appears, said outputs of said lower code disk being divided into said upper and lower groups, said l-th logical circuit having Cr and lo input terminals for respectively receiving said carry signals Cr and lo from said lower code disk and l-1, l and l+1 input terminals for respectively receiving three successive digit signals l-1, l and l+1 from said high order code disk and L output terminal for deriving therefrom said signal corresponding to said digit signal l, said Cr and lo input terminals of each of said n logical circuits being supplied with said carry signals Cr and lo from said L output terminal through said delay circuit, said switching circuit switching connections from said input terminals to said code disks from one code disk to another code disks with predetermined time intervals.
 5. A system for reading digits from an analog-to-digital converter according to claim 4, wherein each of said logical circuits comprises first, second and third NOR circuits respectively coupled to said l, Cr and lo input terminals, a fourth NOR circuit coupled to said l-1 input terminal and to said first and second NOR circuits, a fifth NOR circuit coupled to said Cr and lo input terminals and to said first NOR circuit, a sixth NOR circuit coupled to said l+1 input terminal and to said first and third NOR circuits, a seventh NOR circuit coupled to said fourth, fifth and sixth NOR circuits, and an eighth NOR circuit coupled to said seventh NOR circuit.
 6. A system for reading digits from an analog-to-digital converter according to claim 4, wherein each of said logical circuits comprises a first NOR circuit coupled to said l, Cr and l-1 input terminals, a second NOR circuit coupled to said l, Cr and lo input terminals, a third NOR circuit coupled to said l, lo and l+1 input terminals, and an OR circuit coupled to said first, second and third NOR circuits.
 7. A system for reading digits from an analog-to-digital converter according to claim 4, wherein each of said logical circuits comprises a first NAND circuit coupled to said l, Cr and l-1 input terminals, a second NAND circuit coupled to said l, Cr and lo input terminals, a third NAND circuit coupled to said l, lo and l+1 input terminals, and a fourth NAND circuit coupled to said first, second and third NAND circuits.
 8. A system for reading digits from an analog-to-digital converter according to claim 4, wherein each of said logical circuits comprises of first AND circuit coupled to said l, Cr and l-1 input terminals, a second AND circuit coupled to said l, CR and lo input terminals, a third AND circuit coupled to said l, lo and l+1 input terminals, and an OR circuit coupled to said first, second and third AND circuits. 